Let $x^{2}+y^{2}-4 x-2 y-11=0$ be a circle. A pair of tangents from $(4,5)$ with a pair of radii for

Question

Let $x^{2}+y^{2}-4 x-2 y-11=0$ be a circle. A pair of tangents from $(4,5)$ with a pair of radii form a quadrilateral of area ___ sq units?

Professor PC Thomas Classes · Answer

Let $P Q, P R$ be the tangents to the circle $x^{2}+y^{2}-4 x-2 y-11=0$ from $P(4,5)$\ \ $P Q=P R=\sqrt{16+25-16-10-11}=2$\ $	herefore \quad$ Area of the quadrilateral $=2 	imes$ Area of $	riangle P Q C=2 	imes \frac{1}{2} 	imes 2 	imes 4=8$ sq. units\